Abrams, who averaged 10.7 points last season, will redshirt this season and return to complete his eligibility in 2015-16.
Surgery to repair the injury has yet to be scheduled.
Abrams led the Illini in assists (3.2 per game) and was second in scoring.
"Tracy worked hard in the offseason to put himself in great position heading into his senior year, so he's obviously disappointed and we are for him as well," coach John Groce said in a statement. "But Tracy personifies toughness. He has the heart of a champion and I know that he will only come back stronger from this experience when he returns to the court next year. In the meantime, he will continue to play a vital role for our program with his leadership."
Oregon State transfer Ahmad Starks will likely fill the void at point guard as the Illini attempt to win at least 20 games for the third consecutive season.
Starks averaged 10.4 points and 2.3 assists for the Beavers in 2012-13. He also shot 39 percent from beyond the 3-point line that season.